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In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously.
In classical mechanics, lengths are measured in the same coordinate system.
In classical mechanics, simultaneous also implies one coordinate system.
But in the theory of relativity, the notion of simultaneity is dependent on the observer.
That makes predictions about the future in which many observers are involved very tricky.
Proper distance is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events (or along a timelike path).
That means you need a very clear definition between spacelike versus timelike.

### 1. Proper length or rest length

The proper length or rest length of an object is the length of the object measured by an observer which is at rest relative to it, by applying standard measuring rods on the object.
This is the same as in classical mechanics. When an observer wants to measure something he also has to move?
However, in relatively moving frames the object's endpoints have to be measured simultaneously, since they are constantly changing their position.
What do they mean with end points?
If standard measuring rods are used, the issue is if a measuring rod at rest has the same length as a moving measuring rod. This complexity is not mentioned.
When you want to perform any experiment you should start with two identical rods at rest. The issue is to test if the length stays the same when one is moving. See reference 1

### 2 Proper distance between two events in flat space

The issue is here the distance between two events. That is different between the length of a rod.
In special relativity, the proper distance between two spacelike-separated events is the distance between the two events, as measured in an inertial frame of reference in which the events are simultaneous. In such a specific frame, the distance is given by etc.
In clasical mechanics (with only one coordinate system) general speaking you do not know if two events are simultaneous. You can observe them as simultaneous, but that does not mean they actual are. Of course if they are then the distance is accordingly to the shown formula: ddistance^2 = dx^2 + dy^2 + dz^2.

### Reflection 1 - Lenth contraction

The purpose of the following experiment is to test length contraction. The picture at the left shows two trains.
The first train is identified with the letters B(back) and F(front), which shows the reference train at rest. The length of this train L0 is called the proper length or rest length.
The second train is identified with the letters b and f. The length of this train l should be shorter then L0. The relation should be l = L0/gamma.
 ``` B------X------F --> b---X---f ---> . . . . . . . O ```
In the above setup the observer, at rest, is specific placed perpendicular to the center of the train BF, identified with the letter X. The observer as such sees both ends simultaneous B and F because the distance towards O is the same.
The same for the moving train in the drawn position. In that case he also will see b and f simultaneous, however not at the same instant when the two centers are synchronised but later, because there is a time delay.

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Created: 16 August 2017

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